Vol. 12, No. 4, 2019

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Irreducible character restrictions to maximal subgroups of low-rank classical groups of types $B$ and $C$

Kempton Albee, Mike Barnes, Aaron Parker, Eric Roon and A. A. Schaeffer Fry

Vol. 12 (2019), No. 4, 607–631
DOI: 10.2140/involve.2019.12.607

Representations are special functions on groups that give us a way to study abstract groups using matrices, which are often easier to understand. In particular, we are often interested in irreducible representations, which can be thought of as the building blocks of all representations. Much of the information about these representations can then be understood by instead looking at the trace of the matrices, which we call the character of the representation. This paper will address restricting characters to subgroups by shrinking the domain of the original representation to just the subgroup. In particular, we will discuss the problem of determining when such restricted characters remain irreducible for certain low-rank classical groups.

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irreducible characters, classical groups
Mathematical Subject Classification 2010
Primary: 20C15, 20C33
Received: 12 February 2018
Revised: 11 October 2018
Accepted: 12 October 2018
Published: 16 April 2019

Communicated by Scott T. Chapman
Kempton Albee
Metropolitan State University of Denver
Denver, CO
United States
Mike Barnes
Metropolitan State University of Denver
Denver, CO
United States
Aaron Parker
Metropolitan State University of Denver
Denver, CO
United States
Eric Roon
University of Arizona
Tucson, AZ
United States
A. A. Schaeffer Fry
Department of Mathematical and Computer Sciences
Metropolitan State University of Denver
Denver, CO
United States